You’re saying that a school (or specifically Harvard EA in your case), inclined not to accept you *would change its mind and accept you *because NHS and peer tutoring were listed?
This is a prime example of how HS students’ believe the myth of activities and ECs and their oversized importance to any college.
My answer to your question: no. never.
But since it’ll bug you (esp if you get deferred or rejected), simply shoot an email to Harvard and ask them to kindly insert the note into your file. good luck